Abstract
The Zipoy-Voorhees solution is known as the γ-metric and/or q-metric being static and axisymmetric vacuum solution of Einstein field equations which becomes strong curvature naked singularity. The metric is characterized by two parameters, namely, the mass M and the dimensionless deformation parameter γ. It is shown that the velocity of test particle orbiting around the central γ-object can reach the speed of light, consequently, the total energy of the particle will be very high for a specific value the deformation parameter of the spacetime. It is also shown that causality problem arises in the interior region of the physical singularity for the specific value of the deformation parameter when test particles can move with superluminal velocity being greater than the speed of light that might be an additional tool for explaining the existence of tachyons for γ>1/2 which are invisible for an observer.
Highlights
The mechanisms of the production of high-energy cosmic rays of energy 1020 eV are quite an interesting and important task in modern astrophysics
In the present research note, we have demonstrated that high-energy neutral particles can be generated due to the deformation of the spacetime around the gravitational compact objects which can be in the form of the naked singularity
In the present research note, we have derived the explicit expression for the orbital velocity of test particle in arbitrary spacetime
Summary
The mechanisms of the production of high-energy cosmic rays of energy 1020 eV are quite an interesting and important task in modern astrophysics. It is widely believed that sources of such high-energy cosmic rays are generated by the acceleration of the charged particle in the presence of the external magnetic field in the vicinity of the gravitational compact objects, such as Quasars and Blazars, etc... In the present research note, we have demonstrated that high-energy neutral particles can be generated due to the deformation of the spacetime around the gravitational compact objects which can be in the form of the naked singularity. We derive the expression for the orbital velocity by considering particle motion around the gravitational object described by the Zipoy-Voorhees spacetime [11,12].
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